Bayesian optimization (BO) with Gaussian processes (GP) has become an indispensable algorithm for black box optimization problems. Not without a dash of irony, BO is often considered a black box itself, lacking ways to provide reasons as to why certain parameters are proposed to be evaluated. This is particularly relevant in human-in-the-loop applications of BO, such as in robotics. We address this issue by proposing ShapleyBO, a framework for interpreting BO's proposals by game-theoretic Shapley values.They quantify each parameter's contribution to BO's acquisition function. Exploiting the linearity of Shapley values, we are further able to identify how strongly each parameter drives BO's exploration and exploitation for additive acquisition functions like the confidence bound. We also show that ShapleyBO can disentangle the contributions to exploration into those that explore aleatoric and epistemic uncertainty. Moreover, our method gives rise to a ShapleyBO-assisted human machine interface (HMI), allowing users to interfere with BO in case proposals do not align with human reasoning. We demonstrate this HMI's benefits for the use case of personalizing wearable robotic devices (assistive back exosuits) by human-in-the-loop BO. Results suggest human-BO teams with access to ShapleyBO can achieve lower regret than teams without.

翻译：基于高斯过程（GP）的贝叶斯优化已成为解决黑箱优化问题不可或缺的算法。颇具讽刺意味的是，贝叶斯优化本身常被视为黑箱，缺乏解释为何建议评估特定参数的方法。这一问题在人机协作型贝叶斯优化应用（如机器人领域）中尤为突出。我们提出ShapleyBO框架，通过博弈论中的沙普利值解释贝叶斯优化的建议方案，量化每个参数对贝叶斯优化采集函数的贡献。利用沙普利值的线性性质，我们还能识别各参数对贝叶斯优化的探索与利用行为的影响强度——针对置信界等可加性采集函数。研究发现ShapleyBO可进一步分离探索贡献中的偶然不确定性与认知不确定性成分。此外，该方法催生了基于ShapleyBO的人机交互界面，允许用户在优化建议与人类推理不一致时干预贝叶斯优化过程。通过人机协作型贝叶斯优化实现可穿戴机器人（辅助背部外骨骼）个性化定制的案例，我们验证了该交互界面的优势。结果表明，使用ShapleyBO的人机协同团队比未使用该工具的团队能获得更低的遗憾值。